At Pairing 2010, Lauter et al\'s analysis showed that Ate pairing computation in affine coordinates may be much faster than projective coordinates at high security levels. In this paper, we further investigate techniques to speed up Ate pairing computation in affine coordinates. We first analyze Ate pairing computation using $4$-ary Miller algorithm in affine coordinates. This technique allows us to trade one multiplication in the full extension field and one field inversion for several multiplications in a smaller field. Then, we focus on pairing computations over elliptic curves admitting a twist of degree $3$. We propose new fast explicit formulas for Miller function that are comparable to formulas over even twisted curves. We further analyze pairing computation on cubic twisted curves by proposing efficient subfamilies of pairing-friendly elliptic curves with embedding degrees $k = 9$, and $15$. These subfamilies allow us not only to obtain a very simple form of curve, but also lead to an efficient arithmetic and final exponentiation.

Attribute-based credentials (ABCs) are an important building block of privacy-enhancing identity management. Since non-identifying attributes can easily be abused as the anonymity they provide hides the perpetrator, cryptographic mechanisms need to be introduced to make them revocable. However, most of these techniques are not efficient enough in practice.

ABCs with practical revocation have recently been proposed by Hajny and Malina~\\cite{Hajny-Malina-2012}. Their ABCs make use of different discrete logarithm representations of a fixed value. Although this technique is attractive as the verification of a particular issuer\'s credentials is easy, it has an intrinsic weakness. Colluding users can efficiently forge new credentials that are indistinguishable from legally issued ones.

Recently, Gennaro, Gentry, Parno and Raykova~\\cite{eprint2012:GennaroGPR} proposed an efficient non-interactive zero knowledge argument for Circuit-SAT, based on non-standard notions like conscientious and quadratic span programs. We propose a new non-interactive zero knowledge argument, based on a simple combination of \\emph{standard} span programs (that verify the correctness of every individual gate) and high-distance linear error-correcting codes (that check the consistency of wire assignments). We simplify all steps of the argument. As one of the corollaries, we design an (optimal) wire checker, based on systematic Reed-Solomon codes, of size $8 n$ and degree $4 n$, while the wire checker from~\\cite{eprint2012:GennaroGPR} has size $24 n$ and degree $76 n$, where $n$ is the circuit size. Importantly, the new argument has constant verifier\'s computation.

$line2$ operation, and each operation has 64 steps. The results of two

line operations are combined at the end of every application of the

compression function. In this paper, we present collision

differential characteristics for both $line1$ operation and $line2$ operation by choosing a proper message difference. By using message modification technique seriously, we improve the probabilities of the differential characteristics so that we can give a collision attack on 40-step RIPEMD-128 with a complexity of $2^{35}$ computations.

In 2011, Lindell proposed an efficient commitment scheme, with a non-interactive opening algorithm, in the Universal Composability (UC) framework. He recently acknowledged a bug in its security analysis for the adaptive case. We analyze the proof of the original paper and propose a simple patch of the scheme.

More interestingly, we then modify it and present a more efficient commitment scheme secure in the UC framework, with the same level of security as Lindell\'s protocol: adaptive corruptions, with erasures. The

security is proven in the standard model (with a Common Reference String) under the classical Decisional Diffie-Hellman assumption. Our proposal is the most efficient UC-secure commitment proposed to date (in

We initiate a general study of schemes resilient to both tampering and leakage attacks. Tampering attacks are powerful cryptanalytic attacks where an adversary can change the secret state and observes the effect of such changes at the output. Our contributions are outlined below:

(1) We propose a general construction showing that any cryptographic primitive where the secret key can be chosen as a uniformly random string can be made secure against bounded tampering and leakage. This holds in a restricted model where the tampering functions must be chosen from a set of bounded size after the public parameters have been sampled. Our result covers pseudorandom functions, and many encryption and signature schemes.

(2) We show that standard ID and signature schemes constructed from a large class of Sigma-protocols (including the Okamoto scheme, for instance) are secure even if the adversary can arbitrarily tamper with the prover\'s state a bounded number of times and/or obtain some bounded amount of leakage. Interestingly, for the Okamoto scheme we can allow also independent tampering with the public parameters.

(3) We show a bounded tamper and leakage resilient CCA secure public key cryptosystem based on the DDH assumption. We first define a weaker CPA-like security notion that we can instantiate based on DDH, and then we give a general compiler that yields CCA-security with tamper and leakage resilience. This requires a public tamper-proof common reference string.

(4) Finally, we explain how to boost bounded tampering and leakage resilience (as in 2. and 3. above) to continuous tampering and leakage resilience, in the so-called floppy model where each user has a personal floppy (containing leak- and tamper-free information) which can be used to refresh the secret key (note that if the key is not updated, continuous tamper resilience is known to be impossible). For the case of ID schemes, we also show that if the underlying protocol is secure in the bounded retrieval model, then our compiler remains secure, even if the adversary can tamper with the computation performed by the device.

In some earlier work, the implementation of the tamper resilient primitive was assumed to be aware of the possibility of tampering, in that it would switch to a special mode and, e.g., self-destruct if tampering was detected. None of our results require this assumption.

Bellare, Boldyreva, and O\'Neill (CRYPTO \'07) initiated the study of deterministic public-key encryption as an alternative in scenarios where randomized encryption has inherent drawbacks. The resulting line of research has so far guaranteed security only for adversarially-chosen plaintext distributions that are {\\em independent} of the public key used by the scheme. In most scenarios, however, it is typically not realistic to assume that adversaries do not take the public key into account when attacking a scheme.

We show that it is possible to guarantee meaningful security even for plaintext distributions that depend on the public key. We extend the previously proposed notions of security, allowing adversaries to {\\em adaptively} choose plaintext distributions {\\em after} seeing the public key, in an {\\em interactive} manner. The only restrictions we make are that: (1) plaintext distributions are unpredictable (as is essential in deterministic public-key encryption), and (2) the number of plaintext distributions from which each adversary is allowed to adaptively choose is upper bounded by $2^{p}$, where $p$ can be any predetermined polynomial in the security parameter. For example, with $p = 0$ we capture plaintext distributions that are independent of the public key, and with $p = O(s \\log s)$ we capture, in particular, all plaintext distributions that are samplable by circuits of size $s$.

Within our framework we present both constructions in the random-oracle model based on any public-key encryption scheme, and constructions in the standard model based on lossy trapdoor functions (thus, based on a variety of number-theoretic assumptions). Previously known constructions heavily relied on the independence between the plaintext distributions and the public key for the purposes of randomness extraction. In our setting, however, randomness extraction becomes significantly more challenging once the plaintext distributions and the public key are no longer independent. Our approach is inspired by research on randomness extraction from seed-dependent distributions. Underlying our approach is a new generalization of a method for such randomness extraction, originally introduced by Trevisan and Vadhan (FOCS \'00) and Dodis (PhD Thesis, MIT, \'00).

An often neglected problem for potential practical adoption of Password-based Authenticated Key Exchange (PAKE) protocols on the Internet is the handling of failed password trials. Unlike the currently used approach, where a server-authenticated TLS channel (involving constant number of public key-based operations on both sides) is set up once and can then be used by the client to try a limited number of passwords essentially for free, any new password trial using PAKE would result in the repetition of the entire protocol. With existing PAKE protocols, the minimum number of public key-based operations on both sides is thus lower-bounded by $O(n)$, where $n$ is the number of trials. This bound is optimal for the client (that tries $n$ passwords in the worst case) but is clearly not optimal for the server, which uses the same reference password of the client in each trial. This paper presents a secure and practical approach for achieving the lower bound of $O(1)$ public key operations on the server side.

To this end, we introduce Oblivious PAKE (O-PAKE), a general compiler for a large class of PAKE protocols, allowing a client that shares one password with a server to use a set of passwords within one PAKE session, which succeeds if and only if one of those input passwords matches the one stored on the server side. The term ``oblivious\'\' is used to emphasize that no information about non-matching passwords input by the client is made available to the server, which contrasts for instance to the aforementioned TLS-based approach, where any tried password is disclosed to the server. The $O(1)$ bound on the server side is obtained in our O-PAKE compiler using special processing techniques for the messages of the input PAKE protocol. We prove security of the O-PAKE compiler under standard assumptions using the latest variant of the popular game-based PAKE model by Bellare, Rogaway, and Pointcheval (Eurocrypt 2000). We identify the requirements that PAKE protocols must satisfy in order to suit the compiler and give two concrete O-PAKE protocols based on existing PAKE schemes. Both protocols are implemented and the analysis of their performance attests to the practicality of the compiler.

The use of O-PAKE further eliminates another practical problem with password-based authentication on the Web in that users no longer need to remember the actual association between their frequently used passwords and corresponding servers and can try several of them in one execution without revealing the entire set to the server.

Description: Cryptographic hash functions compute a small fixed-size hash value for any given message. A main application is in digital signatures which require that it must be hard to find collisions, i.e., two different messages that map to the same hash value. In this thesis we provide an analysis of the security of the cryptographic hash function standards MD5 and SHA-1 that have been broken since 2004 due to so called identical-prefix collision attacks. In particular, we present more efficient identical-prefix collision attacks on both MD5 and SHA-1 that improve upon the literature. Furthermore, we introduce a new more flexible attack on MD5 and SHA-1 called the chosen-prefix collision attack that allows significantly more control over the two colliding messages. Moreover, we have proven that our new attack on MD5 poses a realistic threat to the security of everyday applications with our construction of a rogue Certification Authority (CA). Our rogue CA could have enabled the total subversion of secure communications with any website -- if we had not purposely crippled it. Finally, we have introduced an efficient algorithm to detect whether a given message was generated using an identical-prefix or chosen-prefix collision attack on MD5 or SHA-1.[...]

The Centre for Advanced Computing - Algorithms and Cryptography, in the Department of Computing, Faculty of Science, Macquarie University (Sydney, Australia), invites applications for a research fellow in Number Theory and Cryptography